aLAGIS (UMR-CNRS 8146), Ecole Centrale de Lille, Cité Scientifique, 59651 Villeneuve d’Ascq Cedex, France
bLaboratoire de Mathématiques Paul Painlevé (UMR-CNRS 8524), Université de Sciences et Technologies de Lille, France
Abstract:
In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution provides a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function; this is achieved with the converse Lyapunov theorem dedicated to switched systems. In the second part, an explicit construction of a common control Lyapunov function is addressed with respect to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.